Journal
NUCLEAR INSTRUMENTS & METHODS IN PHYSICS RESEARCH SECTION B-BEAM INTERACTIONS WITH MATERIALS AND ATOMS
Volume 266, Issue 8, Pages 1154-1161Publisher
ELSEVIER
DOI: 10.1016/j.nimb.2007.11.057
Keywords
inelastic scattering; Bethe surface; Bethe ridge; dielectric function; energy loss function; water; ice
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The Bethe surface of a material is an essential element in the study of inelastic scattering at low impact energies where the optical approximation fails. In this work we examine various semi-empirical models for the dielectric response function of condensed water towards an improved description of the energy-loss function over the whole energy-momentum plane (i.e. Bethe surface). The experimental optical data (i.e. at zero momentum transfer) for the valence bands of liquid and solid water are analytically represented by a sum-rule constrained linear combination of Drude-type functions. The dependence on momentum transfer is introduced through various widespread extension schemes which are compared against the available Compton scattering data. It is shown that the widely used Lindhard function along with its single-pole (or delta-oscillator) approximation used in the Penn and Ashley models, as well as the Ritchie and Howie extended-Drude scheme with a simple quadratic dispersion, predict a sharp Bethe ridge which compares poorly with the experimental profile. In contrast, the Mermin dielectric function provides a more realistic account of the observed broadening with momentum transfer. An improved fully-extended-Drude model is presented which incorporates the momentum broadening and line-shift of the Bethe ridge and distinguishes between the different dispersion of the discrete and continuum spectra of water. (c) 2007 Elsevier B.V. All rights reserved.
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